9 Answers
9

There has been an association between
the heat and piquancy of mustard and
the zest and energy of people's
behaviour. This dates back to at least
1672, when the term 'as keen as
mustard' is first recorded. 'Up to
mustard' or just 'mustard' means up to
standard in the same way as 'up to
snuff'. 'Cutting' has also long been
used to mean 'exhibiting', as in the
phrase 'cutting a fine figure'. Unless
some actual evidence is found for the
other proposed explanations, the
derivation of 'cutting the mustard' as
an alternative way of saying
'exhibiting one's high standards' is
by far the most likely.

Whatever the coinage, the phrase
itself emerged in the USA towards the
end of the 19th century. The earliest
example in print that I've found is
from The Iowa State Reporter, August
1897, in a piece about the rivalry
between two Iowa towns:

Dubuque had the crowds, but Waterloo
"Cut the Mustard"

The use of quotation marks and the
lack of any explanation of the term in
that citation imply that 'cut the
mustard' was already known to Iowa
readers and earlier printed examples
may yet turn up.

Found this early use of the phrase in a letter from "Rusticus" in The Railroad Trainman, a journal of The Brotherhood of Railroad Trainmen, 1898. In the letter, he reminisces with another letter writer about his days as a trainman which he says started in 1872. He puts in quotes all the slang words and phrases he remembers from those days, of which cut the mustard is one. This may indicate a railroad origin to the phrase. Here's a quote from his letter:

I can cheerfully shake "paws" with him, in my mind, and bring to mind the time when box-toed shoes, squaretopped silk caps and black jeans suits with an inch of braid all around, and spring-bottom pants, were all the "go;" and you could tell a "car-hand" as far as you could see him with the naked eye. And the "pison" he could punish with the "captain" was a caution. Then a "gafter" could buy a job for $10.00, and if he could not "cut the mustard" he was liable to "hit the grit" between stations. Oh, those rosy-hued days, when a brakeman was an important feature about the depot platform about the time the "varnished cars" came in; and what a masher he was.

Edit 6/29/11:

Just found an earlier use of cut the mustard that again seems to indicate a railroad lingo origin. This (see story to rt. of burglary report) is from The Weekly Californian, of Kern County, California, December 3, 1892. It is an account of an anniversary ball put on by the International Association of Machinists. Its use here clearly indicates the "railroad boys" met or exceeded the expected standard of appearance:

The railroad boys were enthusiastic over their apparent success. Each had attended with his best girl looking her prettiest, in fact the boys themselves “cut the mustard” with the Bakersfieldians. The charming costumes of the ladies lent a brightness to the scene, which with the good music did not fail to elicit the appreciation of all present.

The first two quotations in the OED are both from the The Galveston Daily News (Texas, USA). First from 1891:

They applied several coats of carmine hue and cut the mustard over all their predecessors.

Second from 1892:

Time will reveal that he cannot ‘cut the mustard’.

Their definition 3c shows the reasoning and some variants:

slang (orig. U.S.). Something which adds piquancy or zest; that which sets the standard or is the best of anything. to cut the mustard and variants: to come up to expectations, to meet requirements, to succeed. to be (to) the mustard : to be exactly what is required; to be very good or special.

And in the early 20th century are examples like "they were not the proper mustard" and "he's all to the mustard".

There may well be something in the railroad angle here, since wild mustard was regarded as a weed and a crop-destroying pest by farmers in the US — apparently railroad companies were obliged by law to remove it and other weeds from the embankments along the tracks, because it threatened to spread to the surrounding farmland. The Mustard plant is also difficult to physically cut, being a hardy, tough plant...See this aricle from 1908 'Must fight the wild mustard'-

I guess someone who can't 'cut the mustard', is someone (a farmer or railroad company) that can't keep their affairs in order, or keep things neat and tidy, be 'up to scatch'... perhaps similar to the rural phrase 'gone to seed'?

Cut the mustard probably relates to cutting the mustard plant, before it goes to seed, to protect the crops from being over-grown with mustard. The earliest uses of the phrase all cropped up in rural areas - and the context in which the phrase was used is suggestive of the relationship with cutting the plant to prevent it from going to seed, as opposed to "cutting" the prepared mustard sauce for desired taste.

The idiom is known to have emerged in the United States in the late nineteenth century, but the underlying, original meaning of the phrase has not been fully understood. Various explanations have been suggested, including the chore of cutting mustard plants, the difficulty of cutting mustard plants, diluting (cutting) prepared mustard condiments to achieve the proper flavor, or a derivation from the slang use of the word mustard to mean the thing that gives flavor. Although each of the explanations, standing alone, sounds plausible, the evidence, or lack thereof, to support one meaning over another has just not “cut the mustard.” ...

The idiom first appeared in Kansas in 1889, and most of the early examples of its use come from nearby Nebraska, Iowa and Missouri. The location and timing of the development of the idiom, however, does not seem to have been mere happenstance; the seeds of the idiom, actual mustard seeds, had been inadvertently planted about fifteen years earlier, during recovery from the “grasshopper” plagues of 1874 and 1876.

I've heard before that "mustard" was a corruption of "muster", but never found a reliable source or citation for that idea, and the explanation doesn't make much sense anyway. One "passes" muster, one doesn't "cut" it.
– user58110Nov 24 '13 at 16:05

In the pre-civil war US militia system, individuals who failed to appear fit for service were "cut" from the muster. In both British and US usage, units as a whole pass or fail muster.
– TechZenApr 29 '16 at 4:17

In my Canadian experience there was definitely a sub-meaning for "cutting the mustard" that carried more of a sexual meaning. My grandparents made it clear that in their generation that this phrase referred to a man's stamina in the bedroom.

Just an idea:
My dad used the phrase often and 'though I never knew its origin Dad always used it in the sense that one was not up to the task; couldn't be counted upon. He sang a tune:
"He's gettin' too old,
He's gettin' too old,
He's too old to cut the mustard anymore."
One "cuts" too strong liquids to make them useable or palatable, usually with water. Mustard being quite hot may need cutting from time to time and if you're unable, you're not up to the challenge.

Nah. Per JSBangs' answer, cut here is the older sense of exhibit, as in the phrase cut a fine figure. I don't believe for a moment the modern dilute, adulterate sense is relevant, since OED's first citation for this (chiefly American) usage is 1930.
– FumbleFingersOct 6 '13 at 17:39

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